# Ratio word problem

1. Sep 5, 2010

### kazuchan

In order to be included on the ballot in a certain city, a candidate must get at least 12.5% of the registered voters in each of three or more of the city's five districts to sign a petition. The ratio of the numbers of registered voters in the five districts is 6:5:5:4:5. In order for a candidate to be included on a ballet, what is the minimum percent of the total number of registered voters that must sign a petition?

The attempt at a solution
What I tried doing is since they are looking for the minimum percent of the total number of registered voters that must sign the petition, was to look at the smaller numbers in the ratio: 5:4:5 and only these three since they are the smallest and will provide the minimum. I then tried taking the 12.5% and find 12.5% of each ratio but this lead me to nothing.
I am confused on where to go next.
Can you please help me?

2. Sep 6, 2010

### sfskseg32

First, notice that you are given a "ratio" and asked for a "percent." At some point, you're going to have to convert, so lets do it now. Add the numbers in the ratio: 6+5+5+4+5 = 25. There are 25 units of people in the city. That is 100% of the population. Therefore, 1 population unit (ratio) = 4% of the total population. Now express the districts as percents of total population: 24%, 20%, 20%, 16%, 20%.

You were on the right track taking 12.5% of the three smallest districts:
12.5% * (16% + 20% + 20%)
12.5% * 56%
7%

3. Sep 6, 2010

### kazuchan

Thank you for your help! I understand it now!

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